Introduce rational operators and trivial simplification rules.

Trivial simplifications rules (such as "FFa=Fa" or "x&1=x")
are performed any time a formule is instanciated.

* src/ltlast/constant.hh, src/ltlast/constant.cc
(true_instance, true_instance_): Declare the true_instance_ as a
static member, and move true_instance() into the .hh so it gets
inlined.  Have true_instance_ as a class variable will ensure that
it is the first formula instantiated.  Binop simplifications rely
on this to order arguments.
(false_instance, false_instance_): Likewise.
(empty_word_instance, empty_word_instance_): New method and static
member.
* src/ltlast/formula.hh (formula::formula): If max_count_ ever
loops, skip the first three values so that constants always have
smaller hash codes.
* src/ltlast/binop.hh, src/ltlast/binop.cc (instance): Add
simplifications and document them.
* src/ltlast/multop.hh (multop::Concat): New operator.
* src/ltlast/multop.cc (op_name): Handle Concat.
(instance): Inline Concat arguments without reordering.  Handle
absorbent and neutral elements for all operators.
* src/ltlast/unop.hh (unop::Star): New operator.
* src/ltlast/unop.cc (op_name): Handle Star.
(instance): Handle Star, and add trivial simplifications for
other unary operators.
* src/ltlparse/ltlparse.yy (OP_CONCAT, OP_STAR, CONST_EMPTYWORD):
Declare these new operators and add rules for them.
* src/ltlparse/ltlscan.ll (OP_CONCAT, OP_STAR, CONST_EMPTYWORD):
Output these new operators.
* src/ltltest/equals.test: New tests.
* src/ltltest/parse.test: Remove redundant test.
* src/ltltest/tunabbrev.test, src/tgbatest/emptchk.test: Adjust tests.
* src/ltlvisit/basicreduce.cc, src/ltlvisit/contain.cc,
src/ltlvisit/nenoform.cc, src/ltlvisit/reduce.cc,
src/ltlvisit/syntimpl.cc, src/ltlvisit/tostring.cc,
src/ltlvisit/tunabbrev.cc: Complete visitors to handle new
operators.
* src/ltltest/nenoform.test: More tests.
* src/ltlvisit/lunabbrev.cc (unabbreviate_logic_visitor::visit):
Clone formulae before instance() function actually have a chance
to destroy them.
* src/tgba/formula2bdd.cc, src/tgbaalgos/eltl2tgba_lacim.cc,
src/tgbaalgos/ltl2taa.cc, src/tgbaalgos/ltl2tgba_fm.cc,
src/tgbaalgos/ltl2tgba_lacim.cc: Adjust switches to assert on new
operators.

src/ltlast/binop.hh

@@ -56,9 +56,37 @@ namespace spot
 		  M  //< strong release (dual of weak until)
       };
 
-      /// Build an unary operator with operation \a op and
+      /// \brief Build a unary operator with operation \a op and
       /// children \a first and \a second.
-      static binop* instance(type op, formula* first, formula* second);
+      ///
+      /// Some reordering will be performed on arguments of commutative
+      /// operators (Xor and Equiv) to ensure that for instance (a <=> b)
+      /// is the same formula as (b <=> a).
+      ///
+      /// Furthermore, the following trivial simplifications are
+      /// performed (the left formula is rewritten as the right
+      /// formula):
+      ///   - (1 => Exp) = Exp
+      ///   - (0 => Exp) = 0
+      ///   - (Exp => 1) = 1
+      ///   - (Exp => 0) = !Exp
+      ///   - (1 ^ Exp) = !Exp
+      ///   - (0 ^ Exp) = Exp
+      ///   - (0 <=> Exp) = !Exp
+      ///   - (1 <=> Exp) = Exp
+      ///   - (Exp U 1) = 1
+      ///   - (Exp U 0) = 0
+      ///   - (0 U Exp) = Exp
+      ///   - (Exp W 1) = 1
+      ///   - (0 W Exp) = Exp
+      ///   - (1 W Exp) = 1
+      ///   - (Exp R 1) = 1
+      ///   - (Exp R 0) = 0
+      ///   - (1 R Exp) = Exp
+      ///   - (Exp M 0) = 0
+      ///   - (1 M Exp) = Exp
+      ///   - (0 M Exp) = 0
+      static formula* instance(type op, formula* first, formula* second);
 
       virtual void accept(visitor& v);
       virtual void accept(const_visitor& v) const;